# Why fractions are hard

Damn, it's been so long I'm even rustier at this than I thought. I hope all 3 of you are doing well. ## March 27, 2011

As many teachers and parents know, learning the various fraction operations can be difficult for many children. Just look at the amount of rules there are to learn about fractions! Fraction addition - common denominators Add the numerators, and use the common denominator 2. Fraction addition - different denominators First find a common denominator by taking the least common multiple of the denominators.

Then convert all the addends to have this common denominator. Then add using the rule number 1. Finding equivalent fractions Multiply both the numerator and denominator by a same number. Convert a mixed number to a fraction Multiply the whole number part by the denominator and add the numerator to get the numerator.

## COLLECTIONS

Use the common denominator as in the fractional part of the mixed number. Convert an improper fraction to a mixed number Divide the numerator by the denominator to get the whole number part. The remainder will be the numerator of the fractional part. Denominator is the same. Simplifying fractions Find the greatest common divisor of the numerator and denominator, and divide both by Why fractions are hard. Fraction multiplication Multiply the numerators and the denominators. Fraction division Find the reciprocal of the divisor, and multiply by it. Comparing fractions Convert the fractions so they have a common denominator.

Then compare the numerators. Convert fractions to decimals Divide using long division or a calculator. If students simply try to memorize these rules without knowing where they came from, the rules will probably seem like a meaningless jungle.

Students can then become blind followers of the rules, tossing numbers here and there, calculating this and that - and getting answers without having any idea if they are reasonable or not. Besides, it is quite easy to forget these rules or misremember them - especially after years.

That way fractions become something concrete to the student, and not just a number on top of another without a meaning. The student will be able to estimate the answer before calculating, evaluate the reasonableness of the final answer, and perform many of the simplest operations mentally without knowingly applying any "rule.

But that is not enough! We need to have children solve lots of problems using either visual models or fraction manipulatives. Another way is to ask them to DRAW fraction pictures for the problems.

That way the students will form a mental visual model and can think through the pictures. For example, this video shows a visual method for equivalent fractions: If you think through pictures, you will easily see the need for multiplying or dividing both the numerator and denominator by the same number.

They can even have fun splitting the pieces further or conversely merging pieces together. They may find the rule themselves even - and it will make sense. If they forget the rule later, they can always fall back to thinking about splitting the pieces and re-discover it.

Another example is the topic of adding unlike fractions see video. The teacher can show how the pieces in the fractions need to be split further so that they all are the same kind of pieces—and then you can add.

You can simply use pictures or manipulatives. Then, the children will add unlike fractions using manipulatives or by drawing pictures. After a while, some students might discover the rule about the common denominator, or what kind of pieces the fractions will need split into. In any case, they will certainly remember the rule better when they have been able to verify it themselves with numerous visual examples.fractions aren't hard, the human race is simply too stupid to do anything that can be construed as "difficult", like actually thinking.

And that's why the obsession with AI, cuz humans are stupid. To summarize what is known about fraction and decimal arithmetic and to stimulate greater amounts of research in the area, we devoted this review to analyzing why learning fraction and decimal arithmetic is .

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Login with Amazon Try a day free trial of Amazon Prime * Re-login required on Woot! for benefits to take effectPrice: \$ Progressions Documents for the Common Core Math Standards Funded by the Brookhill Foundation Progressions.

Draft Front Matter; Draft K–6 Progression on Geometry. Finding Fractions A whole class tool for finding the fraction of a set of counters. The number of counters is determined by the teacher as is the number coloured red.

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